Existence of a cointegration relationship between two time series in the time domain imposes restrictions on the series zero-frequency behaviour in terms of their squared coherence, phase, and gain, in the frequency domain. I derive these restrictions by studying cross-spectral properties of a cointegrated bivariate system. Specifically, I demonstrate that if two difference stationary series, X(t) and Y(t), are cointegrated with a cointegrating vector [1 b] and thus share a common stochastic trend, then at the zero frequency, the squared coherence of (1 - L) X(t) and (1 - L) Y(t) will equal one, their phase will equal zero, and their gain will equal |b|.
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Paper provided by EconWPA in its series Econometrics with number
0402005.
Length: 14 pages Date of creation: 07 Feb 2004 Date of revision: Handle: RePEc:wpa:wuwpem:0402005
Note: Type of Document - pdf; prepared on Win 98; to print on Any printer; pages: 14 ; figures: There are no figures Contact details of provider: Web page: http://129.3.20.41
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